Comparison and analysis of techniques to address nonlinearity and non-stationarity in correlations of economic and financial time series

Abstract

In many of the economic and financial behavior there is an interest in determining the relationships between variables, to order to build explanatory theories, conducting forecasts, optimization, etc. However, many of the situations have placed non-linear behavior, in which traditional techniques are not indicated because capture only linear correlations. Besides the aspect of non-linearity, the most common behavior observed in economic and financial time series is not stationary. Again, there are several techniques in Econometrics that are only able to address successfully stationary series. This project aims to analyze the correlation of the time series of the stock market during the period of the subprime crisis, which will be considered temporally between the years 2008 and 2010, and their neighborhoods. Initially, expected to be possible to identify changes in structure of the correlations due to the transition between the periods considered. To analyze these series, with its characteristics of non-stationary and non-linearity, will be used alternative techniques such as Random Matrix Theory and Detrended Cross-Correlation Analysis. The Random Matrix Theory serves as a filter for the correlation, so as to provide a separation between noise and the really significant correlations by means of spectral analysis of eigenvalues of the matrices. But the method of Detrended Cross-Correlation Analysis is an extension of Detrended Fluctuation Analysis of concept for application in more than a time series, establishing the kind of long-term correlation between the series under study, from a power law between covariance and the number of the time series partitions that are used to perform the withdrawal of trend. (AU)